The standard research strategy for studying intellectual development is to present a problem to children of different ages, and to examine the differences in the way they approach it. This strategy, however, provides little information on how children get from one stage of functioning to the next. An alternative strategy is to teach children how to approach a problem, and to study the process by which their functioning increases in efficiency. The difficulty with this strategy is that it provides little information on how such changes might occur in a more naturalistic setting. The present proposal describes a new research paradigm in which both these problems are eliminated. Two procedures for using the paradigm are possible, experimental and clinical. To explore the utility of the experimental approach, a study is proposed which will examine the extent to which a child's response to a naturalistic learning opportunity is a function of his level of general development. To explore the utility of the clinical approach, a study is proposed which will assess the role of "equilibration" in the process of spontaneous development. On the assumption that both of these approaches will prove fruitful, a method is also described for extending the procedures and generalizing the results.